Participial

I'm teaching basic participial constructions now, but, with regard to those below, what different ways of translating them would everybody use?

§ 280. A Participial is a derived form of the verb used not for asserting but for expressing either, — 1. An object of thought; or, 2. A modification of such an object. Participials, accordingly, are either, — 1. Noun-participials; as, "To think is to act;" "Their sending the messacre was the cause of the trouble;" or, 2. Adjective-participials, more commonly called Participles; as, "The advancing army;" "The expected messenger."

[…] the verb has two forms, which […] are called Participials, namely, (a) The Infinitv […] (b) The Participle […] .

To have a short appellation, let us call participles and infinitives participials. Among all the myriads of words, a more skillful, many-sided and hard-working class than this could hardly be found, and still—such is the world's reward—they are strangers in a strange land forced to live with their aristocratic cousins, the "finite" verbs. For participials are not verbs in reality.